Main issue is that if a card removed from the field can't resolve it's effect. That's a question I have. If so, is Bombardment a valid target to send it off, even though it has no hearts? If not, then paying the cost is viable even at 0 hearts, as it's not left the field yet.
K. As above, spells can activate at 0 hearts just fine. Being at 0 hearts doesn't really inhibit effects.
Generally, that's because the effect is one that activates automatically when the card enters play, or as a consequence of reaching 0 hearts. The difference is this one is an effect that has to be activated manually. Like, consider Magic the Gathering. If a card receives lethal damage, one doesn't get to just say "okay but hold on, let me tap it to activate this ability first,
then I'll send it to my Graveyard", that's something any player would readily call an opponent out for doing.
Of course, this isn't MtG, and I won't speak
for Supernerd on this front, but generally it's considered bad or awkward game design to allow a card to just ignore its destruction until after its player has decided they got enough value out of it. Of course, this is where the card Fog of War gets really awkward, because its effects can be activated 'in any order' implying multiple 'windows' of action taking place in the space of that one cast. Honestly, that's the sort of thing I would have considered vetoing for being
too complicated.